radiative transfer theory at optical and microwave wavelengths applied to vegetation canopies: part...
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Radiative Transfer Theory at Optical and Microwave wavelengths applied to
vegetation canopies: part 1
UoL MSc Remote Sensing
course tutors: Dr Lewis [email protected]
Dr Saich [email protected]
Aim of this section
• Introduce RT approach as basis to understanding optical and microwave vegetation response
• enable use of models
• enable access to literature
Scope of this section
• Introduction to background theory– RT theory– Wave propagation and polarisation– Useful tools for developing RT
• Building blocks of a canopy scattering model– canopy architecture– scattering properties of leaves– soil properties
Associated practical and reading
• Reading– microwave leaf model
• Chuah, H.T., Lee, K.Y., and Lau, T.W., 1995, “Dielectric constants of rubber and oil palm leaf samples at X-band”, IEEE Trans. Geoscience and Remote Sensing, GE-33, 221-223.
– Optical leaf model• Jacquemoud, S., and Baret, F., 1990, “PROSPECT: a model of leaf
optical properties spectra”, Remote Sensing of Environment, 34, 75-91.
• Practicals investigating leaf scattering– Optical OR microwave
Why build models?
• Assist data interpretation• calculate RS signal as fn. of biophysical variables
• Study sensitivity• to biophysical variables or system parameters
• Interpolation or Extrapolation• fill the gaps / extend observations
• Inversion• estimate biophysical parameters from RS
• aid experimental design• plan experiments
Radiative Transfer Theory
• Approach optical and microwave case at same time through RT– ‘relatively’ simple & well-understood– no other treatment in this way– researchers tend to specialise in either field
• less understanding of other field / synergy
• Deal with other approaches in later lectures
Radiative Transfer Theory
• Applicability– heuristic treatment
• consider energy balance across elemental volume
– assume:• no correlation between fields
– addition of power not fields
• no diffraction/interference in RT– can be in scattering
– develop common (simple) case here
Radiative Transfer Theory
• Case considered:– horizontally infinite but vertically finite plane
parallel medium (air) embedded with infinitessimal oriented scattering objects at low density
– canopy lies over soil surface (lower boundary)– assume horizontal homogeneity
• applicable to many cases of vegetation
Radiative Transfer Theory
• More accurate approach is to use Maxwell’s equations
• difficult to formulate
• will return to for object scattering but not propagation (RT)
Radiative Transfer Theory
• More accurate approach is to use Maxwell’s equations
• difficult to formulate
• will return to for object scattering but not propagation (RT)
Radiative Transfer Theory
• More accurate approach is to use Maxwell’s equations
• difficult to formulate
• use object scattering but not propagation (RT)
• essentially wave equation for electric field
• k - wavenumber = 2/ in air
02 zEkdz
zEd ikz
h
v eE
EzE
Plane wave
Radiative Transfer Theory
• Consider incident Electric-field Ei(r) of magnitude Ei in direction to a position r:
• incident wave sets up internal currents in scatterer that reradiate ‘scattered’ wave
• Remote sensing problem:– describe field received at a sensor from an area
extensive ensemble average of scatterers
k̂
rkikirkik
ih
ivi eEe
E
ErE
ˆˆ
Scattering
• Define using scattering matrix:
• elements polarised scattering amplitudes– for discs:
– for needles:
• assume scattering in far field
i
hhvhv
vhvvrik
irik
s ESS
SS
r
eES
r
eE
00
x
xJnorientatio
VkS dpq
120 0.2,
4
1
x
xnorientatio
VkS npq
sin,
4
120
Scattering
x
xJnorientatio
VkS dpq
120 0.2,
4
1
Bessel function
(complex) permittivity of leaf
Leaf volumeWavenumber2 = 42/2
Scattering
x
xnorientatio
VkS npq
sin,
4
120
Sinc function
Stokes Vector
• Can represent plane wave polarisation by , and phase term:
• h,v phase equal for linear polarised wave
ihEi
vE
rkikirkik
ih
ivi eEe
E
ErE
ˆˆ
Stokes Vector
• More convenient to use modified Stokes vector:
*
*
2
2
Im2
Re2
hv
hv
h
v
h
v
m
EE
EE
E
E
V
U
I
I
F
Stokes Vector
• Using this, relate scattered Stokes vector to incident:
im
im
rm FW
rF
rF 1
22
11
hhvvvhvvhhhvhhvvv
vhhvvvhhvhhhvvhv
hhhvhvhhhhhhhvhv
vhvvvvvhvhvhvvvv
SSSSSSSS
SSSSSSSS
SSSSSSSS
SSSSSSSS
W
****
****
****
****
ii00
1100
0011
0011
N.B S2 so 1/4 for discs etc
Stokes Vector
• Average Mueller matrix over all scatterers to obtain phase matrix for use in RT
Building blocks for a canopy model
• Require descriptions of:– canopy architecture– leaf scattering– soil scattering
Soil
H
zCanopy
Canopy Architecture• 1-D: Functions of depth from the top of the canopy (z).
Canopy Architecture• 1-D: Functions of depth from the top of the canopy (z).
1. Vertical leaf area density (m2/m3)
OR
the vertical leaf number density function, Nv(z) (number of particles per m3)
2. the leaf normal orientation distribution function, (dimensionless).
3. leaf size distribution• defined as:
– area to relate leaf area density to leaf number density, as well as thickness. – the dimensions or volume of prototype scattering objects such as discs, spheres, cylinders or
needles.
zul
Canopy Architecture
• Leaf area / number density– (one-sided) m2 leaf per m3
– Nv(z) - number of ‘particles’ per m3
zul
lvl AzNzu
dzzuLHz
z
l
0
LAI
l
x
z
y
ql
fl
Inclination to vertical
azimuth
Leaf normal vector
Canopy Architecture• Leaf Angle Distribution
12
lll dg
• Archetype Distributions:planophile
erectophile
spherical
plagiophile
extremophile
Leaf Angle Distribution
lllg 2cos3
lllg 2sin2
3
1llg
lllg 2sin8
15 2
lllg 2cos7
15 2
• Archetype Distributions:
Leaf Angle Distribution
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 10 20 30 40 50 60 70 80 90
g_
l(t
he
ta
_l)
leaf zenith angle / degrees
spherical planophile erectophileplagiophile extremophile
• Elliptical Distribution:
Leaf Angle Distribution
2122 sin1 ml
llg
eccentricity of distribution : 10mmodal leaf angle : 2
0m
• Elliptical Distribution:Leaf Angle Distribution
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 10 20 30 40 50 60 70 80 90
g_
l(t
he
ta
_l)
leaf zenith angle / degrees
erectophile planophile plagiophile
Elliptical leaf angle distributions:=0.9; qm=0 (erectophile), /2 (planophile), /4 (plagiophile)
• RT theory: infinitessimal scatterers– without modifications (dealt with later)
• Scattering at microwave depends on leaf volume for given number per unit area– on leaf ‘thickness’ for given LAI
• In optical, leaf size affects canopy scattering in retroreflection direction– ‘roughness’ term: ratio of leaf linear dimension to canopy height
also, leaf thickness effects on reflectance /transmittance
Leaf Dimension
• RT theory: infinitessimal scatterers– without modifications (dealt with later)
• Scattering at microwave depends on leaf volume for given number per unit area– on leaf ‘thickness’ for given LAI
• In optical, leaf size affects canopy scattering in retroreflection direction– ‘roughness’ term: ratio of leaf linear dimension to canopy height
also, leaf thickness effects on reflectance /transmittance
Leaf Dimension
Canopy element and soil spectral properties
• Scattering properties of leaves– scattering affected by:
• Leaf surface properties and internal structure;
• leaf biochemistry;
• leaf size (essentially thickness, for a given LAI).
Scattering properties of leaves
• Leaf surface properties and internal structure
Dicotyledon leaf structure
opticalSpecular
from surface
Smooth (waxy) surface- strong peak
hairs, spines- more diffused
Scattering properties of leaves
• Leaf surface properties and internal structure
Dicotyledon leaf structure
opticalDiffused
from scattering at internal air-cell wall interfaces
Depends on refractive index:varies: 1.5@400 nm
1.3@2500nmDepends on total areaof cell wall interfaces
Scattering properties of leaves
• Leaf surface properties and internal structure
Dicotyledon leaf structure
optical
More complex structure (or thickness):- more scattering- lower transmittance- more diffuse
Scattering properties of leaves
• Leaf surface properties and internal structure
Dicotyledon leaf structure
microwave
Thickness (higher volume)- higher scattering
Scattering properties of leaves
• Leaf biochemstry
Scattering properties of leaves• Leaf biochemstry
Scattering properties of leaves• Leaf biochemstry
Scattering properties of leaves• Leaf biochemstry
Scattering properties of leaves
• Leaf biochemstry– pigments: chlorophyll a and b, -carotene, and
xanthophyll • absorb in blue (& red for chlorophyll)
– absorbed radiation converted into:• heat energy, flourescence or carbohydrates through
photosynthesis
Scattering properties of leaves
• Leaf biochemstry– Leaf water is major consituent of leaf fresh weight,
• around 66% averaged over a large number of leaf types
– other constituents ‘dry matter’• cellulose, lignin, protein, starch and minerals
– Absorptance constituents increases with concentration• reducing leaf reflectance and transmittance at these
wavelengths.
Scattering properties of leaves• Optical Models
– flowering plants: PROSPECT
Scattering properties of leaves• Optical Models
– flowering plants: PROSPECT
Scattering properties of leaves• Leaf water
Scattering properties of leaves
• Leaf water PROSPECT:
leaf water content parameterised as equivalent water thickness (EWT) approximates the water mass per unit leaf area. related to volumetric moisture content (VMC, Mv)
(proportionate volume of water in the leaf) by multiplying EWT by the product of leaf thickness and water density.
Scattering properties of leaves
• Microwave:– water content related to leaf permittivity, .
25.62.37.1 vvn MM
166.082.0 vvf MMvf
2
2
5.591
4.31
v
vb M
Mvf
18.01
559.2
18
181
759.4
fi
vff
if
ivfM bfnv
Volume fractions
Offset factor
Scattering properties of leaves
• Microwave:– water content related to leaf permittivity, .
18.01
559.2
18
181
759.4
fi
vff
if
ivfM bfnv
Frequency / GHz
iconic conductivity of free water
Scattering properties of leaves
• leaf dimensions– optical
• increase leaf area for constant number of leaves - increase LAI
• increase leaf thickness - decrease transmittance (increase reflectance)
– microwave• leaf volume dependence of scattering
– volume for constant leaf number
– thickness for constant leaf area
Scattering properties of soils
• Optical and microwave affected by:– soil moisture content– soil type/texture– soil surface roughness.
soil moisture content• Optical
– effect essentially proportional across all wavelengths• enhanced in water absorption bands
soil moisture content
• Microwave– increases soil dielectric constant
• effect varies with wavelength
• generally increases volume scattering – and decreases penetration depth
soil texture/type• Optical
– relatively little variation in spectral properties– Price (1985):
• PCA on large soil database• 99.6% of variation in 4 PCs
– Stoner & Baumgardner (1982) defined 5 main soil types:• organic dominated• minimally altered• iron affected• organic dominated• iron dominated
• Microwave - affects dielectric constant
Soil roughness effects• Simple models:
– as only a boundary condition, can sometimes use simple models
• e.g. Lambertian
• e.g. trigonometric (Walthall et al., 1985)
Soil roughness effects• Smooth surface:
– Fresnel specular reflectance/transmittance– can be important at microwave
• due to double bounce in forest
– can be important at optical for viewing in close to specular direction
– Using Stokes vector:
ir IRI12
Soil roughness effects• Smooth surface:
12*
1212*
12
12*
1212*
12
2
12
2
12
12
ReIm00
ImRe00
000
000
hvhv
hvhv
h
v
rrrr
rrrr
r
r
R
2211
221112
2112
211212
coscos
coscos
coscos
coscos
nn
nnr
nn
nnr
h
v
1122 sinsin nn
Soil roughness effects
• Low roughness:– use low magnitude distribution of facets
• apply specular scattering over distribution
– general effect:• increases angular width of specular peak
Soil roughness effects
• Rough roughness:– optical surface scattering
• clods, rough ploughing– use Geometric Optics model (Cierniewski)
– projections/shadowing from protrusions
Soil roughness effects
• Rough roughness:– optical surface scattering
• Note backscatter reflectance peak (‘hotspot’)
• minimal shadowing
• backscatter peak width increases with increasing roughness
Soil roughness effects
• Rough roughness:– volumetric scattering
• consider scattering from ‘body’ of soil– particulate medium
– use RT theory (Hapke - optical)
– modified for surface effects (at different scales of roughness)
Summary• Introduction
– Examined rationale for modelling– discussion of RT theory– Scattering from leaves– Stokes vector/Mueller matrix
• Canopy model building blocks– canopy architecture: area/number, angle, size– leaf scattering: spectral & structural– soil scattering: roughness, type, water